Obfuscation: Building the final boss of cryptography (Part I)

I’m reasonably familiar with cryptography but the formalism of obfuscation given here makes no sense to me.

> The precise formalism typically used, indistinguishability obfuscation, says that if you are given obfuscations of two different programs that have the same functionality, you can't tell which is which.

This seems… not that useful? A sufficiently advanced optimizing compiler would be capable of transforming two input programs with identical functionality into one or the other, or both into some third representation. Either approach meets this criteria but doesn’t seem to me to provide any useful purpose.

And in practice, do two identically-functioning but different programs even exist in the wild? Two superficially identical programs of nontrivial complexity will almost certainly have divergent behavior somewhere (bugs, edge cases), at which point this formalism becomes moot.